where \(\langle n\rangle \)  is mean photon number and \(\Delta n\)  is standard deviation of the photon number. It is well known that the Mandel parameter is directly related with physical properties[1]}: Optical spin coherent state (OS-CS)[2]}, Barut-Girardello CS (BG-CS)[3]} and modified Susskind-Glogower coherent state (mSG-CS)[4]}, [5]} has negative Mandel parameter (\(Q_M^{\vec{h}}<0\) ). This implies that OS-CS, BG-CS and mSG-CS are sub-Poissoninan. Meanwhile, Perelomov coherent state (P-CS) has negative Mandel parameter (\(Q_M^{\vec{h}}>0\) ). This implies that P-CS is super-Poissonian. As sub-Poissonianity of NS-CS can improve the Helstrom bound[1]}, we mainly focus on the sub-Poissonian NS-CS.
